Adjuvant trials report hazard ratios, but treatment decisions need absolute risk differences. It is important to recognise that the two align only when baseline risk is uniform across the treated population. The decision on whether to use anthracyclines as adjuvant chemotherapy in early breast cancer illustrates this point acutely: the same average relative effect prevents several recurrences in one patient and almost none in another, while the risk of cardiac toxicity increases in the opposite direction.
This issue is highly topical in early breast cancer since the first results from the OPTIMA trial, reported at the 2026 American Society of Clinical Oncology (ASCO) meeting, showed that Prosigna-directed treatment allocation was non-inferior to chemotherapy-for-all and that 68% of tested patients could safely be spared chemotherapy altogether (J Clin Oncol 2026). Genomic assays now routinely decide who receives chemotherapy, and the oncology community is re-focusing on risk-informed decision making using this information. Here, we look at the related decision on which chemotherapy, and for whom the anthracycline is the correct choice given its risk of cardiac toxicity. That decision rests on the same logic of baseline risk, and the hazard ratio alone struggles to inform this conversation well.
Why does a constant hazard ratio produce unequal absolute benefit?
Under proportional hazards a hazard ratio applies equally to every patient, whatever their underlying risk, and this is why the Early Breast Cancer Trialists’ Collaborative Group (EBCTCG) found proportional reductions in breast cancer mortality from polychemotherapy to be little affected by age, nodal status, tumour diameter or differentiation, or oestrogen receptor status (Lancet 2012). Absolute benefit is a different quantity, since it is that same ratio applied to a baseline risk which varies from patient to patient. The EBCTCG highlight that gains from a one-third reduction in mortality depend on the absolute risk a woman faces without chemotherapy, so a low absolute risk implies a low absolute benefit. Their later update showed that adding anthracycline concurrently to docetaxel and cyclophosphamide cut ten-year recurrence from 21.0% to 12.3%, a risk difference of 8.7 per 100 women treated (95% CI 4.5 to 12.9; Lancet 2023). That figure is an average across the trial populations, and it does not tell us where within the spread of baseline risk those 8.7 events per 100 actually arise.
What does the additive hazards model estimate?
Cox regression fits hazard ratios on the multiplicative scale, so its interaction terms describe deviation from multiplicativity rather than from additivity of absolute effects. Rod and colleagues set out the alternative methodological framing, in which the hazard is specified as a sum of a baseline term and effect terms rather than as a product, so that the deviation from additivity of absolute effects is estimated directly and carries its own confidence interval (Epidemiology 2012). This is the quantity that identifies which subgroup carries most of the preventable events. A treatment can hold a constant hazard ratio across every subgroup and still show strong additive interaction, because additive interaction describes where the absolute risk difference concentrates, and that concentration follows baseline risk even when the relative effect never moves.
In plainer terms, a treatment that removes a third of a patient’s risk prevents 10 recurrences per 100 women whose risk was 30 per 100, and 1 recurrence per 100 women whose risk was 3 per 100. The multiplicative scale records the third, which is the same for both groups. The additive scale records the 10 and the 1.
When does the relative effect itself change? Recurrence score versus age and nodal status
Age and nodal status are prognostic markers, which set baseline risk without moving the chemotherapy hazard ratio, so that absolute benefit changes only because a fixed multiplier meets a different baseline. The 21-gene recurrence score behaved differently in the analysis Chen and colleagues published from TAILORx. Among participants with a recurrence score of 31 or higher, adding anthracycline to taxane-based chemotherapy improved the five-year distant recurrence-free interval from 91.0% with docetaxel and cyclophosphamide to 96.1% with a taxane-anthracycline regimen, an adjusted hazard ratio of 0.31 (P=0.006; Ann Oncol 2025), and spline regression showed the benefit rising continuously with score. That is a predictive relationship, in which the relative effect itself moves rather than a fixed effect meeting a moving baseline. The same class of assay that identified who could forgo chemotherapy in OPTIMA may therefore also identify who gains most from intensifying it. The comparison was not randomised, since the regimen reflected physician choice within a population already randomised to chemotherapy itself, and it carries the confounding caveat set out below.
What does cardiac harm look like on the absolute scale?
Cardiac harm follows the same logic, being a relative hazard multiplied onto a baseline that varies by patient. Goldhar and colleagues found that adjuvant trastuzumab raised the five-year cumulative incidence of heart failure from 2.5% to 5.2%, with no multiplicative interaction from anthracycline use (interaction P=0.92 within the first 1.5 years; JNCI 2016). Bowles and colleagues put the adjusted hazard ratio for heart failure or cardiomyopathy after anthracycline plus trastuzumab at 7.19 relative to no chemotherapy (95% CI 5.00 to 10.35; JNCI 2012). That ratio applies to a baseline cardiac hazard which comorbidity itself raises. In a SEER-Medicare cohort of 43,338 women aged 66 to 80 with early breast cancer, Pinder and colleagues reported hazard ratios for congestive heart failure of 1.45 for hypertension, 1.74 for diabetes and 1.58 for coronary artery disease, so comorbidity enters as a further multiplier on the same underlying rate (J Clin Oncol 2007). A comorbid patient starts from a higher cardiac baseline, so the same relative cardiotoxicity produces more absolute heart failure. Battisti and colleagues showed the resulting gradient directly, with cardiotoxicity reaching 30.3% at high or very high cardiovascular risk on the HFA-ICOS tool against 14.0% at low risk, although severe heart failure remained uncommon, with NYHA class III-IV events in 0.5% and no cardiac deaths among 931 patients (Breast Cancer Res Treat 2021).
Why do competing risks make this more of an issue?
Comorbidity acts in two ways – it raises the baseline cardiac hazard against which the relative excess from anthracycline multiplies, and it also raises the competing hazard of death from other causes before a prevented recurrence could ever occur. A recurrence averted in year four is of no value to a patient who has died of cardiovascular disease in year three. Competing non-cancer mortality therefore erodes the realisable recurrence benefit in precisely those patients whose comorbidity is inflating the cardiac harm, so that the two effects compound rather than offset one another. Standard survival analysis, which censors at the competing event, overstates the benefit a comorbid patient can expect. The additive framework extends into this setting through cumulative incidence regression, which keeps the estimate on the absolute scale while accounting properly for the competing event. Communication matters here as much as estimation. Risk-informed decision making of the kind OPTIMA represents reaches the patient only if the oncologist can interpret risk and competing risk together and present both per 100 patients like themselves, since a shared decision about anthracycline rests on that framing rather than on a hazard ratio.
An illustrative comparison
The table below is an illustrative composite rather than a validated risk-prediction tool. It applies the estimates above to two hypothetical patients, mixing source populations and follow-up horizons in order to demonstrate the arithmetic rather than to estimate an individual effect.
| Patient A: 55 years, recurrence score 35, no cardiac risk factors | Patient B: 74 years, recurrence score 18, hypertension and diabetes | |
|---|---|---|
| Recurrences prevented per 100 treated with anthracycline, 5 years | 5.1 | 0.6 |
| Heart failure cases added per 100 treated with anthracycline, 5 years | 0.8 | 2.0 |
Patient A’s figures come directly from the recurrence-score-31-or-above arm of Chen and colleagues, at 9.0 per 100 without anthracycline against 3.9 with it. Patient B’s assume a baseline distant recurrence risk of 4 per 100 without anthracycline, to which the EBCTCG’s 14% relative reduction for concurrent anthracycline-taxane regimens is applied. The cardiac figures for both patients begin from an assumed baseline heart failure risk of 2 per 100 over five years without chemotherapy, at age 55 and with no cardiac risk factors. That baseline is multiplied by Pinder and colleagues’ hypertension and diabetes hazard ratios to reach Patient B’s starting point, and then by Bowles and colleagues’ hazard ratio of 1.40 for anthracycline alone against no chemotherapy to obtain the cases added.
What caveats limit this argument?
Confounding by indication is an issue. Comorbid and older patients are already steered away from anthracycline in routine practice, a pattern Chen and colleagues describe in their own cohort, so an observational comparison by comorbidity status risks recovering the clinician’s existing judgement rather than the drug’s independent effect. The Bowles and Pinder hazard ratios rest on claims-identified heart failure, a looser definition than the adjudicated, echocardiography-based endpoints Battisti and colleagues used, so their absolute figures probably run high. The OPTIMA result is an interim analysis with immature follow-up, and it addresses whether to give chemotherapy rather than which regimen to give. The comparison table mixes populations, horizons and treatment eras, and demonstrates arithmetic rather than predicting an individual outcome. No published study has yet applied the additive hazards model directly to recurrence score or cardiovascular comorbidity in the anthracycline decision, and the reasoning set out here indicates what such an estimate might show without standing in for one.
Software and the next step
The R package timereg implements the additive hazards model described here. The function aalen() fits Aalen’s additive hazards model with time-varying effects and confidence bands, returning the additive deviation directly, while comp.risk() extends the same additive link into the competing risks setting and fits cumulative incidence regression, so that recurrence and non-cancer death compete for the same patient-time (J Stat Softw 2011). Fine and Gray’s proportional subdistribution hazards model is recoverable within the same comp.risk() framework as the proportional special case, by switching the link from additive to multiplicative. The next step is to fit that additive model directly to trial or registry data stratified by recurrence score and cardiovascular comorbidity, rather than combining published estimates by hand as the table above does.
References
- Stein RC, Makris A, Macpherson IR, Hughes-Davies L, Marshall A, Pinder SE, et al. First results from the OPTIMA phase III randomized non-inferiority trial of test-directed chemotherapy in patients with high clinical risk ER-positive HER2-negative early breast cancer. J Clin Oncol. 2026;44(16_suppl):500. doi:10.1200/JCO.2026.44.16_suppl.500
- Early Breast Cancer Trialists’ Collaborative Group (EBCTCG). Comparisons between different polychemotherapy regimens for early breast cancer: meta-analyses of long-term outcome among 100 000 women in 123 randomised trials. Lancet. 2012;379(9814):432-44. doi:10.1016/S0140-6736(11)61625-5
- Early Breast Cancer Trialists’ Collaborative Group (EBCTCG). Anthracycline-containing and taxane-containing chemotherapy for early-stage operable breast cancer: a patient-level meta-analysis of 100 000 women from 86 randomised trials. Lancet. 2023;401(10384):1277-92. doi:10.1016/S0140-6736(23)00285-4
- Rod NH, Lange T, Andersen I, Marott JL, Diderichsen F. Additive interaction in survival analysis. Epidemiology. 2012;23(5):733-7. doi:10.1097/EDE.0b013e31825fa218
- Chen N, Freeman JQ, Yarlagadda S, Atmakuri A, Kalinsky K, Pusztai L, et al. Impact of anthracyclines in genomic high-risk, node-negative, HR-positive/HER2-negative breast cancer. Ann Oncol. 2025;36(11):1356-65. doi:10.1016/j.annonc.2025.08.002
- Goldhar HA, Yan AT, Ko DT, Earle CC, Tomlinson GA, Trudeau ME, et al. The temporal risk of heart failure associated with adjuvant trastuzumab in breast cancer patients: a population study. J Natl Cancer Inst. 2016;108(1):djv301. doi:10.1093/jnci/djv301
- Bowles EJA, Wellman R, Feigelson HS, Onitilo AA, Freedman AN, Delate T, et al. Risk of heart failure in breast cancer patients after anthracycline and trastuzumab treatment: a retrospective cohort study. J Natl Cancer Inst. 2012;104(17):1293-305. doi:10.1093/jnci/djs317
- Pinder MC, Duan Z, Goodwin JS, Hortobagyi GN, Giordano SH. Congestive heart failure in older women treated with adjuvant anthracycline chemotherapy for breast cancer. J Clin Oncol. 2007;25(25):3808-15. doi:10.1200/JCO.2006.10.4976
- Battisti NML, Andres MS, Lee KA, Ramalingam S, Nash T, Mappouridou S, et al. Incidence of cardiotoxicity and validation of the Heart Failure Association-International Cardio-Oncology Society risk stratification tool in patients treated with trastuzumab for HER2-positive early breast cancer. Breast Cancer Res Treat. 2021;188(1):149-63. doi:10.1007/s10549-021-06192-w
- Scheike TH, Zhang MJ. Analyzing competing risk data using the R timereg package. J Stat Softw. 2011;38(2):1-15. doi:10.18637/jss.v038.i02